AUSTIN - Central Texas’ strong housing market did not disappoint in September, as home sales jumped nearly 34 percent last month — the most single-family home sales for September since 2005.

According to the Austin Board of Realtors, 2,391 sales closed in September, a 33.5 percent increase from the 1,791 sales in September 2012. The median price last month was $223,000, 13 percent higher than in September 2012, when it was $197,500.

Jim Gaines, a research economist at Texas A&M University’s Real Estate Center, said that with the region’s job and population growth, there isn’t enough housing inventory to meet the current demand.

On a month-over-month basis, sales were down about 19 percent from August. However, homes sold faster than they did a year ago, spending 44 days on the market on average versus 66 days in September 2012.

Year-to-date through September, the median sales price in Austin was up 9 percent, twice the local annual average, Gaines said.